Solve for $x$ and $y$ using substitution. ${x+5y = -7}$ ${y = -x+1}$
Solution: Since $y$ has already been solved for, substitute $-x+1$ for $y$ in the first equation. ${x + 5}{(-x+1)}{= -7}$ Simplify and solve for $x$ $x-5x + 5 = -7$ $-4x+5 = -7$ $-4x+5{-5} = -7{-5}$ $-4x = -12$ $\dfrac{-4x}{{-4}} = \dfrac{-12}{{-4}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = -x+1}\thinspace$ to find $y$ ${y = -}{(3)}{ + 1}$ $y = -3 + 1$ $y = -2$ You can also plug ${x = 3}$ into $\thinspace {x+5y = -7}\thinspace$ and get the same answer for $y$ : ${(3)}{ + 5y = -7}$ ${y = -2}$